The all-or-none character of transmission at central synapses is commonly viewed as evidence that only one vesicle can be released per action potential at a single release site. This interpretation is still a matter of debate; its resolution is important for our understanding of the nature of quantal response. In this work we explore observable consequences of the univesicular release hypothesis by studying a stochastic model of synaptic transmission. We investigated several alternative mechanisms for the all-or-none response: (1) the univesicular release constraint realized through lateral inhibition across presynaptic membrane, (2) the constraint of a single releasable vesicle per active zone, and (3) the postsynaptic receptor saturation. We show that both the univesicular release constraint and the postsynaptic receptor saturation lead to a limited amount of depression by vesicle depletion, so that depletion alone cannot account for the strong paired-pulse depression observed at some cortical synapses. Although depression can be rapid if there is only one releasable vesicle per active zone, this scenario leads to a limit on the transmission probability. We evaluate additional mechanisms beyond vesicle depletion, and our results suggest that the strong paired-pulse depression may be a result of activity-dependent inactivation of the exocytosis machinery. Furthermore, we found that the statistical analysis of release events, in response to a long stimulus train, might allow one to distinguish experimentally between univesicular and multivesicular release scenarios. We show that without the univesicular release constraint, the temporal correlation between release events is always negative, whereas it is typically positive with such a constraint if the vesicle fusion probability is sufficiently large.

Presynaptic terminals favor intermediate-conductance Ca(V)2.2 (N type) over high-conductance Ca(V)1 (L type) channels for single-channel, Ca(2+) nanodomain-triggered synaptic vesicle fusion. However, the standard Ca(V)1>Ca(V)2>Ca(V)3 conductance hierarchy is based on recordings using nonphysiological divalent ion concentrations. We found that, with physiological Ca(2+) gradients, the hierarchy was Ca(V)2.2>Ca(V)1>Ca(V)3. Mathematical modeling predicts that the Ca(V)2.2 Ca(2+) nanodomain, which is ∼25% more extensive than that generated by Ca(V)1, can activate a calcium-fusion sensor located on the proximal face of the synaptic vesicle.

We investigate the complex-temperature singularities of the susceptibility of the 2D Ising model on a square lattice. From an analysis of low-temperature series expansions, we find evidence that as one approaches the point u = u s = −1 (where u = e −4K ) from within the complex extensions of the FM or AFM phases, the susceptibility has a divergent singularity of the form χ ∼ A s = 2 is satisfied. However, using exact results for β s on the square, triangular, and honeycomb lattices, we show that universality is violated at this singularity: β s is lattice-dependent. Finally, from an analysis of spin-spin correlation functions, we demonstrate that the correlation length and hence susceptibility are finite as one approaches the point u = −1 from within the symmetric phase. This is confirmed by an explicit study of high-temperature series expansions. *

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